Chase Berry csb4319

Week 10 6.2.8

6.2.8

Which statements are correct? Give counterexamples to justify the statements you exclude

Is sure to equal

a. orthogonal

b. a basis for a vector space containing v.

c. orthonormal

- both b and c

Solution:

a.False.

If u is the set of orthogonal vectors, one of the vectors could be on the plane while another one of the vectors could be off of the plane. The above term expression represents the orthogonal projection. Then, its orthogonal projection will be on the plane, but then that projection will not equal itself.

b. False—The coefficient formula is wrong in this case

- False

This is the same as part a except the vectors are of unit length. It still doesn’t work. The length has nothing to do with it in this case.

d. True.